472 ON PHYSICAL LINES OF FORCE. 



Let the horizontal circle MM' represent a line of magnetic force embracing 

 the electric circuit, the north and south directions being indicated by the lines 

 SN and NS. 



Let the vertical circles V and V represent the molecular vortices of which 

 the line of magnetic force is the axis. V revolves as the hands of a watch, 

 and V the opposite way. 



It will appear from this diagram, that if V and V were contiguous vortices, 

 particles placed between them would move downwards ; and that if the particles 

 were forced downwards by any cause, they would make the vortices revolve as 

 in the figure. We have thus obtained a point of view from which we may 

 regard the relation of an electric current to its lines of force as analogous to 

 the relation of a toothed wheel or rack to wheels which it drives. 



In the first part of the paper we investigated the relations of the statical 

 forces of the system. We have now considered the connexion of the motions 

 of the parts considered as a system of mechanism. It remains that we should 

 investigate the dynamics of the system, and determine the forces necessary to 

 produce given changes in the motions of the different parts. 



PROP. VI. To determine the actual energy of a portion of a medium due 

 to the motion of the vortices within it. 



Let a, /3, y be the components of the circumferential velocity, as in Prop. II., 

 then the actual energy of the vortices in unit of volume will be proportional 

 to the density and to the square of the velocity. As we do not know the 

 distribution of density and velocity in each vortex, we cannot determine the 

 numerical value of the energy directly ; but since p also bears a constant 

 though unknown ratio to the mean density, let us assume that the energy 

 in unit of volume is 



where C is a constant to be determined. 

 Let us take the case in which 



dx ' dy ' ' dz ' 

 Let < = <, + <, (36), 



